LMFDB - Embedded newform 540.2.n.d.179.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(179,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.179"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-2,18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.6
Character	$\chi$	$=$	540.179
Dual form			540.2.n.d.359.6

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00727 - 0.992675i) q^{2} +(0.0291929 + 1.99979i) q^{4} +(0.493735 - 2.18088i) q^{5} +(-1.65751 - 2.87089i) q^{7} +(1.95573 - 2.04331i) q^{8} +(-2.66223 + 1.70662i) q^{10} +(-1.17952 - 2.04298i) q^{11} +(3.81058 + 2.20004i) q^{13} +(-1.18030 + 4.53714i) q^{14} +(-3.99830 + 0.116759i) q^{16} -0.889368 q^{17} +3.03537i q^{19} +(4.37570 + 0.923698i) q^{20} +(-0.839925 + 3.22872i) q^{22} +(-6.29952 - 3.63703i) q^{23} +(-4.51245 - 2.15355i) q^{25} +(-1.65437 - 5.99870i) q^{26} +(5.69278 - 3.39848i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(0.205172 + 0.118456i) q^{31} +(4.14327 + 3.85140i) q^{32} +(0.895835 + 0.882853i) q^{34} +(-7.07943 + 2.19737i) q^{35} -11.4975i q^{37} +(3.01314 - 3.05745i) q^{38} +(-3.49059 - 5.27407i) q^{40} +(-2.45213 - 1.41574i) q^{41} +(-4.17637 - 7.23369i) q^{43} +(4.05110 - 2.41842i) q^{44} +(2.73494 + 9.91686i) q^{46} +(-6.55796 + 3.78624i) q^{47} +(-1.99467 + 3.45488i) q^{49} +(2.40749 + 6.64861i) q^{50} +(-4.28837 + 7.68457i) q^{52} +0.772055 q^{53} +(-5.03787 + 1.56369i) q^{55} +(-9.10776 - 2.22789i) q^{56} +(1.63908 + 0.426394i) q^{58} +(-1.06446 + 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(-0.0890754 - 0.322986i) q^{62} +(-0.350216 - 7.99233i) q^{64} +(6.67943 - 7.22417i) q^{65} +(-3.17238 + 5.49472i) q^{67} +(-0.0259632 - 1.77855i) q^{68} +(9.31218 + 4.81423i) q^{70} +11.7244 q^{71} +6.10889i q^{73} +(-11.4133 + 11.5811i) q^{74} +(-6.07010 + 0.0886114i) q^{76} +(-3.91012 + 6.77253i) q^{77} +(8.94873 - 5.16655i) q^{79} +(-1.71946 + 8.77744i) q^{80} +(1.06459 + 3.86020i) q^{82} +(-2.25103 + 1.29963i) q^{83} +(-0.439112 + 1.93960i) q^{85} +(-2.97396 + 11.4321i) q^{86} +(-6.48127 - 1.58541i) q^{88} +4.68130i q^{89} -14.5863i q^{91} +(7.08939 - 12.7039i) q^{92} +(10.3642 + 2.69615i) q^{94} +(6.61978 + 1.49867i) q^{95} +(-5.34684 + 3.08700i) q^{97} +(5.43875 - 1.49994i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) $ 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00727	−	0.992675i	−0.712249	−	0.701927i
$2$	−1.00727	−	0.992675i	−0.712249	−	0.701927i
$3$		0			0
$3$		0			0
$4$	0.0291929	+	1.99979i	0.0145965	+	0.999893i
$5$	0.493735	−	2.18088i	0.220805	−	0.975318i
$5$	0.493735	−	2.18088i	0.220805	−	0.975318i
$6$		0			0
$7$	−1.65751	−	2.87089i	−0.626480	−	1.08509i	−0.988253	−	0.152828i	$-0.951162\pi$
$7$	−1.65751	−	2.87089i	−0.626480	−	1.08509i	0.361773	−	0.932266i	$-0.382172\pi$
$8$	1.95573	−	2.04331i	0.691456	−	0.722418i
$9$		0			0
$10$	−2.66223	+	1.70662i	−0.841870	+	0.539680i
$11$	−1.17952	−	2.04298i	−0.355638	−	0.615983i	0.631589	−	0.775303i	$-0.282403\pi$
$11$	−1.17952	−	2.04298i	−0.355638	−	0.615983i	−0.987227	+	0.159320i	$0.949070\pi$
$12$		0			0
$13$	3.81058	+	2.20004i	1.05686	+	0.610181i	0.924563	−	0.381029i	$-0.124430\pi$
$13$	3.81058	+	2.20004i	1.05686	+	0.610181i	0.132301	+	0.991210i	$0.457763\pi$
$14$	−1.18030	+	4.53714i	−0.315448	+	1.21260i
$15$		0			0
$16$	−3.99830	+	0.116759i	−0.999574	+	0.0291898i
$17$	−0.889368			−0.215703			−0.107852	−	0.994167i	$-0.534397\pi$
$17$	−0.889368			−0.215703			−0.107852	+	0.994167i	$0.534397\pi$
$18$		0			0
$19$			3.03537i			0.696363i	0.937427	+	0.348181i	$0.113201\pi$
$19$			3.03537i			0.696363i	−0.937427	+	0.348181i	$0.886799\pi$
$20$	4.37570	+	0.923698i	0.978437	+	0.206545i
$21$		0			0
$22$	−0.839925	+	3.22872i	−0.179073	+	0.688365i
$23$	−6.29952	−	3.63703i	−1.31354	−	0.758374i	−0.330861	−	0.943680i	$-0.607339\pi$
$23$	−6.29952	−	3.63703i	−1.31354	−	0.758374i	−0.982681	+	0.185306i	$0.940672\pi$
$24$		0			0
$25$	−4.51245	−	2.15355i	−0.902490	−	0.430710i
$26$	−1.65437	−	5.99870i	−0.324448	−	1.17644i
$27$		0			0
$28$	5.69278	−	3.39848i	1.07583	−	0.642251i
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	−0.593195	−	0.805059i	$-0.702134\pi$
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	0.400604	+	0.916251i	$0.368800\pi$
$30$		0			0
$31$	0.205172	+	0.118456i	0.0368499	+	0.0212753i	0.518312	−	0.855192i	$-0.326561\pi$
$31$	0.205172	+	0.118456i	0.0368499	+	0.0212753i	−0.481462	+	0.876467i	$0.659894\pi$
$32$	4.14327	+	3.85140i	0.732434	+	0.680838i
$33$		0			0
$34$	0.895835	+	0.882853i	0.153634	+	0.151408i
$35$	−7.07943	+	2.19737i	−1.19664	+	0.371423i
$36$		0			0
$37$		−	11.4975i		−	1.89018i	−0.326807	−	0.945091i	$-0.605973\pi$
$37$		−	11.4975i		−	1.89018i	0.326807	−	0.945091i	$-0.394027\pi$
$38$	3.01314	−	3.05745i	0.488796	−	0.495983i
$39$		0			0
$40$	−3.49059	−	5.27407i	−0.551911	−	0.833903i
$41$	−2.45213	−	1.41574i	−0.382958	−	0.221101i	0.296146	−	0.955143i	$-0.404298\pi$
$41$	−2.45213	−	1.41574i	−0.382958	−	0.221101i	−0.679105	+	0.734042i	$0.737632\pi$
$42$		0			0
$43$	−4.17637	−	7.23369i	−0.636891	−	1.10313i	−0.986111	−	0.166087i	$-0.946887\pi$
$43$	−4.17637	−	7.23369i	−0.636891	−	1.10313i	0.349220	−	0.937041i	$-0.386447\pi$
$44$	4.05110	−	2.41842i	0.610726	−	0.364591i
$45$		0			0
$46$	2.73494	+	9.91686i	0.403245	+	1.46216i
$47$	−6.55796	+	3.78624i	−0.956577	+	0.552280i	−0.895118	−	0.445829i	$-0.852909\pi$
$47$	−6.55796	+	3.78624i	−0.956577	+	0.552280i	−0.0614594	+	0.998110i	$0.519575\pi$
$48$		0			0
$49$	−1.99467	+	3.45488i	−0.284954	+	0.493554i
$50$	2.40749	+	6.64861i	0.340470	+	0.940255i
$51$		0			0
$52$	−4.28837	+	7.68457i	−0.594689	+	1.06566i
$53$	0.772055			0.106050			0.0530249	−	0.998593i	$-0.483114\pi$
$53$	0.772055			0.106050			0.0530249	+	0.998593i	$0.483114\pi$
$54$		0			0
$55$	−5.03787	+	1.56369i	−0.679306	+	0.210848i
$56$	−9.10776	−	2.22789i	−1.21708	−	0.297715i
$57$		0			0
$58$	1.63908	+	0.426394i	0.215222	+	0.0559883i
$59$	−1.06446	+	1.84370i	−0.138581	+	0.240029i	−0.926960	−	0.375161i	$-0.877587\pi$
$59$	−1.06446	+	1.84370i	−0.138581	+	0.240029i	0.788379	+	0.615190i	$0.210921\pi$
$60$		0			0
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	0.962114	−	0.272647i	$-0.0878990\pi$
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	−0.717176	+	0.696892i	$0.754566\pi$
$62$	−0.0890754	−	0.322986i	−0.0113126	−	0.0410193i
$63$		0			0
$64$	−0.350216	−	7.99233i	−0.0437769	−	0.999041i
$65$	6.67943	−	7.22417i	0.828481	−	0.896048i
$66$		0			0
$67$	−3.17238	+	5.49472i	−0.387567	+	0.671287i	−0.992122	−	0.125277i	$-0.960018\pi$
$67$	−3.17238	+	5.49472i	−0.387567	+	0.671287i	0.604554	+	0.796564i	$0.293351\pi$
$68$	−0.0259632	−	1.77855i	−0.00314851	−	0.215680i
$69$		0			0
$70$	9.31218	+	4.81423i	1.11302	+	0.575410i
$71$	11.7244			1.39143			0.695717	−	0.718316i	$-0.255087\pi$
$71$	11.7244			1.39143			0.695717	+	0.718316i	$0.255087\pi$
$72$		0			0
$73$			6.10889i			0.714992i	0.933915	+	0.357496i	$0.116369\pi$
$73$			6.10889i			0.714992i	−0.933915	+	0.357496i	$0.883631\pi$
$74$	−11.4133	+	11.5811i	−1.32677	+	1.34628i
$75$		0			0
$76$	−6.07010	+	0.0886114i	−0.696288	+	0.0101644i
$77$	−3.91012	+	6.77253i	−0.445600	+	0.771802i
$78$		0			0
$79$	8.94873	−	5.16655i	1.00681	−	0.581283i	0.0965546	−	0.995328i	$-0.469218\pi$
$79$	8.94873	−	5.16655i	1.00681	−	0.581283i	0.910256	+	0.414045i	$0.135884\pi$
$80$	−1.71946	+	8.77744i	−0.192242	+	0.981348i
$81$		0			0
$82$	1.06459	+	3.86020i	0.117565	+	0.426288i
$83$	−2.25103	+	1.29963i	−0.247083	+	0.142653i	−0.618428	−	0.785842i	$-0.712230\pi$
$83$	−2.25103	+	1.29963i	−0.247083	+	0.142653i	0.371345	+	0.928495i	$0.378897\pi$
$84$		0			0
$85$	−0.439112	+	1.93960i	−0.0476284	+	0.210379i
$86$	−2.97396	+	11.4321i	−0.320690	+	1.23275i
$87$		0			0
$88$	−6.48127	−	1.58541i	−0.690906	−	0.169006i
$89$			4.68130i			0.496217i	0.968732	+	0.248108i	$0.0798089\pi$
$89$			4.68130i			0.496217i	−0.968732	+	0.248108i	$0.920191\pi$
$90$		0			0
$91$		−	14.5863i		−	1.52906i
$92$	7.08939	−	12.7039i	0.739120	−	1.32447i
$93$		0			0
$94$	10.3642	+	2.69615i	1.06898	+	0.278087i
$95$	6.61978	+	1.49867i	0.679175	+	0.153760i
$96$		0			0
$97$	−5.34684	+	3.08700i	−0.542890	+	0.313438i	−0.746249	−	0.665667i	$-0.768147\pi$
$97$	−5.34684	+	3.08700i	−0.542890	+	0.313438i	0.203360	+	0.979104i	$0.434814\pi$
$98$	5.43875	−	1.49994i	0.549397	−	0.151517i
$99$		0			0
$100$	4.17491	−	9.08681i	0.417491	−	0.908681i
$101$	6.72336	−	3.88174i	0.669000	−	0.386247i	−0.126698	−	0.991941i	$-0.540438\pi$
$101$	6.72336	−	3.88174i	0.669000	−	0.386247i	0.795697	+	0.605694i	$0.207105\pi$
$102$		0			0
$103$	6.58033	−	11.3975i	0.648379	−	1.12302i	−0.335131	−	0.942171i	$-0.608781\pi$
$103$	6.58033	−	11.3975i	0.648379	−	1.12302i	0.983510	−	0.180853i	$-0.0578860\pi$
$104$	11.9478	−	3.48350i	1.17158	−	0.341585i
$105$		0			0
$106$	−0.777669	−	0.766400i	−0.0755339	−	0.0744393i
$107$		−	0.252175i		−	0.0243786i	−0.999926	−	0.0121893i	$-0.996120\pi$
$107$		−	0.252175i		−	0.0243786i	0.999926	−	0.0121893i	$-0.00388008\pi$
$108$		0			0
$109$	0.459068			0.0439708			0.0219854	−	0.999758i	$-0.493001\pi$
$109$	0.459068			0.0439708			0.0219854	+	0.999758i	$0.493001\pi$
$110$	6.62674	+	3.42590i	0.631835	+	0.326647i
$111$		0			0
$112$	6.96242	+	11.2851i	0.657886	+	1.06635i
$113$	8.71557	−	15.0958i	0.819892	−	1.42009i	−0.0858696	−	0.996306i	$-0.527367\pi$
$113$	8.71557	−	15.0958i	0.819892	−	1.42009i	0.905761	−	0.423788i	$-0.139300\pi$
$114$		0			0
$115$	−11.0422	+	11.9428i	−1.02969	+	1.11367i
$116$	−1.22773	−	2.05657i	−0.113992	−	0.190948i
$117$		0			0
$118$	2.90240	−	0.800444i	0.267187	−	0.0736868i
$119$	1.47414	+	2.55328i	0.135134	+	0.234059i
$120$		0			0
$121$	2.71748	−	4.70681i	0.247043	−	0.427891i
$122$	1.36225	−	5.23657i	0.123332	−	0.474097i
$123$		0			0
$124$	−0.230897	+	0.413758i	−0.0207352	+	0.0371565i
$125$	−6.92458	+	8.77782i	−0.619354	+	0.785112i
$126$		0			0
$127$	10.5666			0.937635			0.468817	−	0.883295i	$-0.344680\pi$
$127$	10.5666			0.937635			0.468817	+	0.883295i	$0.344680\pi$
$128$	−7.58102	+	8.39810i	−0.670074	+	0.742294i
$129$		0			0
$130$	−13.8993	+	0.646199i	−1.21905	+	0.0566754i
$131$	8.12900	−	14.0798i	0.710234	−	1.23016i	−0.254535	−	0.967064i	$-0.581922\pi$
$131$	8.12900	−	14.0798i	0.710234	−	1.23016i	0.964769	−	0.263098i	$-0.0847444\pi$
$132$		0			0
$133$	8.71423	−	5.03116i	0.755619	−	0.436257i
$134$	8.64991	−	2.38554i	0.747239	−	0.206079i
$135$		0			0
$136$	−1.73937	+	1.81725i	−0.149149	+	0.155828i
$137$	6.59587	+	11.4244i	0.563523	+	0.976051i	0.997185	+	0.0749753i	$0.0238878\pi$
$137$	6.59587	+	11.4244i	0.563523	+	0.976051i	−0.433662	+	0.901076i	$0.642779\pi$
$138$		0			0
$139$	−5.61535	−	3.24202i	−0.476288	−	0.274985i	0.242580	−	0.970131i	$-0.422006\pi$
$139$	−5.61535	−	3.24202i	−0.476288	−	0.274985i	−0.718868	+	0.695146i	$0.755340\pi$
$140$	−4.60093	−	14.0932i	−0.388850	−	1.19109i
$141$		0			0
$142$	−11.8097	−	11.6385i	−0.991047	−	0.976685i
$143$		−	10.3799i		−	0.868014i
$144$		0			0
$145$	0.793820	+	2.55751i	0.0659232	+	0.212390i
$146$	6.06415	−	6.15332i	0.501872	−	0.509252i
$147$		0			0
$148$	22.9926	−	0.335646i	1.88998	−	0.0275900i
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	0.172708	−	0.984973i	$-0.444748\pi$
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	−0.766658	+	0.642056i	$0.778082\pi$
$150$		0			0
$151$	14.2008	−	8.19886i	1.15565	−	0.667214i	0.205391	−	0.978680i	$-0.434153\pi$
$151$	14.2008	−	8.19886i	1.15565	−	0.667214i	0.950257	+	0.311466i	$0.100820\pi$
$152$	6.20220	+	5.93638i	0.503065	+	0.481504i
$153$		0			0
$154$	10.6615	−	2.94030i	0.859127	−	0.236936i
$155$	0.359638	−	0.388968i	0.0288868	−	0.0312427i
$156$		0			0
$157$	9.27700	+	5.35608i	0.740386	+	0.427462i	0.822209	−	0.569185i	$-0.192741\pi$
$157$	9.27700	+	5.35608i	0.740386	+	0.427462i	−0.0818239	+	0.996647i	$0.526075\pi$
$158$	−14.1425	−	3.67906i	−1.12512	−	0.292690i
$159$		0			0
$160$	10.4451	−	7.13440i	0.825758	−	0.564024i
$161$			24.1137i			1.90042i
$162$		0			0
$163$	1.33584			0.104631			0.0523153	−	0.998631i	$-0.483340\pi$
$163$	1.33584			0.104631			0.0523153	+	0.998631i	$0.483340\pi$
$164$	2.75959	−	4.94507i	0.215488	−	0.386145i
$165$		0			0
$166$	3.55752	+	0.925458i	0.276117	+	0.0718295i
$167$	6.20942	+	3.58501i	0.480500	+	0.277417i	0.720625	−	0.693325i	$-0.243855\pi$
$167$	6.20942	+	3.58501i	0.480500	+	0.277417i	−0.240125	+	0.970742i	$0.577188\pi$
$168$		0			0
$169$	3.18034	+	5.50851i	0.244641	+	0.423731i
$170$	2.36770	−	1.51781i	0.181594	−	0.116411i
$171$		0			0
$172$	14.3439	−	8.56303i	1.09371	−	0.652925i
$173$	−1.28765	−	2.23027i	−0.0978979	−	0.169564i	0.812916	−	0.582380i	$-0.197879\pi$
$173$	−1.28765	−	2.23027i	−0.0978979	−	0.169564i	−0.910814	+	0.412816i	$0.864545\pi$
$174$		0			0
$175$	1.29682	+	16.5243i	0.0980307	+	1.24912i
$176$	4.95460	+	8.03074i	0.373467	+	0.605340i
$177$		0			0
$178$	4.64701	−	4.71534i	0.348308	−	0.353430i
$179$	−10.1847			−0.761243			−0.380622	−	0.924731i	$-0.624290\pi$
$179$	−10.1847			−0.761243			−0.380622	+	0.924731i	$0.624290\pi$
$180$		0			0
$181$	4.17537			0.310353			0.155176	−	0.987887i	$-0.450405\pi$
$181$	4.17537			0.310353			0.155176	+	0.987887i	$0.450405\pi$
$182$	−14.4795	+	14.6924i	−1.07329	+	1.08907i
$183$		0			0
$184$	−19.7518	+	5.75880i	−1.45612	+	0.424545i
$185$	−25.0747	−	5.67673i	−1.84353	−	0.417362i
$186$		0			0
$187$	1.04902	+	1.81696i	0.0767123	+	0.132870i
$188$	−7.76312	−	13.0040i	−0.566184	−	0.948414i
$189$		0			0
$190$	−5.18022	−	8.08086i	−0.375813	−	0.586247i
$191$	12.5152	+	21.6770i	0.905570	+	1.56849i	0.820151	+	0.572147i	$0.193889\pi$
$191$	12.5152	+	21.6770i	0.905570	+	1.56849i	0.0854186	+	0.996345i	$0.472777\pi$
$192$		0			0
$193$	−16.3830	−	9.45871i	−1.17927	−	0.680853i	−0.223426	−	0.974721i	$-0.571724\pi$
$193$	−16.3830	−	9.45871i	−1.17927	−	0.680853i	−0.955846	+	0.293868i	$0.905057\pi$
$194$	8.45011	+	2.19823i	0.606683	+	0.157824i
$195$		0			0
$196$	−6.96725	−	3.88807i	−0.497661	−	0.277719i
$197$	−5.25418			−0.374345			−0.187172	−	0.982327i	$-0.559932\pi$
$197$	−5.25418			−0.374345			−0.187172	+	0.982327i	$0.559932\pi$
$198$		0			0
$199$			18.8487i			1.33615i	0.744095	+	0.668074i	$0.232881\pi$
$199$			18.8487i			1.33615i	−0.744095	+	0.668074i	$0.767119\pi$
$200$	−13.2255	+	5.00856i	−0.935185	+	0.354159i
$201$		0			0
$202$	−10.6256	−	2.76415i	−0.747612	−	0.194485i
$203$	3.43813	+	1.98500i	0.241309	+	0.139320i
$204$		0			0
$205$	−4.29825	+	4.64879i	−0.300203	+	0.324686i
$206$	−17.9421	+	4.94821i	−1.25009	+	0.344758i
$207$		0			0
$208$	−15.4927	−	8.35148i	−1.07423	−	0.579071i
$209$	6.20122	−	3.58028i	0.428948	−	0.247653i
$210$		0			0
$211$	−3.96081	−	2.28678i	−0.272674	−	0.157428i	0.357428	−	0.933941i	$-0.383654\pi$
$211$	−3.96081	−	2.28678i	−0.272674	−	0.157428i	−0.630102	+	0.776512i	$0.716987\pi$
$212$	0.0225385	+	1.54395i	0.00154795	+	0.106039i
$213$		0			0
$214$	−0.250327	+	0.254008i	−0.0171120	+	0.0173636i
$215$	−17.8378	+	5.53663i	−1.21653	+	0.377595i
$216$		0			0
$217$		−	0.785367i		−	0.0533142i
$218$	−0.462407	−	0.455706i	−0.0313181	−	0.0308643i
$219$		0			0
$220$	−3.27412	−	10.0290i	−0.220741	−	0.676156i
$221$	−3.38900	−	1.95664i	−0.227969	−	0.131618i
$222$		0			0
$223$	11.8767	+	20.5711i	0.795323	+	1.37754i	0.922634	+	0.385677i	$0.126032\pi$
$223$	11.8767	+	20.5711i	0.795323	+	1.37754i	−0.127310	+	0.991863i	$0.540634\pi$
$224$	4.18943	−	18.2786i	0.279918	−	1.22129i
$225$		0			0
$226$	−23.7642	+	6.55386i	−1.58077	+	0.435956i
$227$	24.1252	−	13.9287i	1.60124	−	0.924478i	0.610005	−	0.792398i	$-0.291168\pi$
$227$	24.1252	−	13.9287i	1.60124	−	0.924478i	0.991239	−	0.132081i	$-0.0421658\pi$
$228$		0			0
$229$	8.35991	−	14.4798i	0.552439	−	0.956852i	−0.445659	−	0.895203i	$-0.647031\pi$
$229$	8.35991	−	14.4798i	0.552439	−	0.956852i	0.998098	−	0.0616492i	$-0.0196360\pi$
$230$	22.9778	−	1.06827i	1.51511	−	0.0704399i
$231$		0			0
$232$	−0.804848	+	3.29027i	−0.0528409	+	0.216017i
$233$	1.67938			0.110020			0.0550101	−	0.998486i	$-0.482481\pi$
$233$	1.67938			0.110020			0.0550101	+	0.998486i	$0.482481\pi$
$234$		0			0
$235$	5.01943	+	16.1715i	0.327432	+	1.05491i
$236$	−3.71808	−	2.07487i	−0.242027	−	0.135063i
$237$		0			0
$238$	1.04972	−	4.03518i	0.0680432	−	0.261562i
$239$	−5.41085	+	9.37186i	−0.349999	+	0.606215i	−0.986249	−	0.165267i	$-0.947151\pi$
$239$	−5.41085	+	9.37186i	−0.349999	+	0.606215i	0.636250	+	0.771483i	$0.280485\pi$
$240$		0			0
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	0.635022	−	0.772494i	$-0.280991\pi$
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	−0.986510	+	0.163698i	$0.947658\pi$
$242$	−7.40957	+	2.04346i	−0.476305	+	0.131359i
$243$		0			0
$244$	−6.57037	+	3.92238i	−0.420625	+	0.251104i
$245$	6.54982	+	6.05593i	0.418453	+	0.386899i
$246$		0			0
$247$	−6.67794	+	11.5665i	−0.424907	+	0.735961i
$248$	0.643303	−	0.187561i	0.0408498	−	0.0119101i
$249$		0			0
$250$	15.6885	−	1.96779i	0.992225	−	0.124454i
$251$	5.05766			0.319237			0.159618	−	0.987179i	$-0.448974\pi$
$251$	5.05766			0.319237			0.159618	+	0.987179i	$0.448974\pi$
$252$		0			0
$253$			17.1598i			1.07883i
$254$	−10.6434	−	10.4892i	−0.667829	−	0.658151i
$255$		0			0
$256$	15.9727	−	0.933676i	0.998296	−	0.0583548i
$257$	6.69541	−	11.5968i	0.417649	−	0.723388i	−0.578054	−	0.815999i	$-0.696188\pi$
$257$	6.69541	−	11.5968i	0.417649	−	0.723388i	0.995702	+	0.0926101i	$0.0295210\pi$
$258$		0			0
$259$	−33.0081	+	19.0573i	−2.05103	+	1.18416i
$260$	14.6418	+	13.1465i	0.908045	+	0.815314i
$261$		0			0
$262$	−22.1648	+	6.11278i	−1.36935	+	0.377649i
$263$	9.43213	−	5.44564i	0.581610	−	0.335793i	−0.180163	−	0.983637i	$-0.557663\pi$
$263$	9.43213	−	5.44564i	0.581610	−	0.335793i	0.761773	+	0.647844i	$0.224329\pi$
$264$		0			0
$265$	0.381190	−	1.68376i	0.0234163	−	0.103432i
$266$	−13.7719	−	3.58265i	−0.844410	−	0.219666i
$267$		0			0
$268$	−11.0809	−	6.18367i	−0.676872	−	0.377728i
$269$		−	21.5020i		−	1.31100i	−0.755195	−	0.655500i	$-0.772458\pi$
$269$		−	21.5020i		−	1.31100i	0.755195	−	0.655500i	$-0.227542\pi$
$270$		0			0
$271$		−	18.9445i		−	1.15080i	−0.817873	−	0.575399i	$-0.804847\pi$
$271$		−	18.9445i		−	1.15080i	0.817873	−	0.575399i	$-0.195153\pi$
$272$	3.55595	−	0.103842i	0.215611	−	0.00629634i
$273$		0			0
$274$	4.69686	−	18.0550i	0.283748	−	1.09074i
$275$	0.922846	+	11.7590i	0.0556497	+	0.709096i
$276$		0			0
$277$	−16.1616	+	9.33092i	−0.971058	+	0.560641i	−0.899559	−	0.436800i	$-0.856112\pi$
$277$	−16.1616	+	9.33092i	−0.971058	+	0.560641i	−0.0714994	+	0.997441i	$0.522778\pi$
$278$	2.43791	+	8.83982i	0.146216	+	0.530177i
$279$		0			0
$280$	−9.35558	+	18.7629i	−0.559103	+	1.12130i
$281$	5.84683	−	3.37567i	0.348792	−	0.201375i	−0.315361	−	0.948972i	$-0.602126\pi$
$281$	5.84683	−	3.37567i	0.348792	−	0.201375i	0.664153	+	0.747596i	$0.268792\pi$
$282$		0			0
$283$	2.63488	−	4.56374i	0.156627	−	0.271286i	−0.777023	−	0.629472i	$-0.783271\pi$
$283$	2.63488	−	4.56374i	0.156627	−	0.271286i	0.933650	+	0.358186i	$0.116605\pi$
$284$	0.342270	+	23.4464i	0.0203100	+	1.39129i
$285$		0			0
$286$	−10.3039	+	10.4554i	−0.609283	+	0.618242i
$287$			9.38639i			0.554061i
$288$		0			0
$289$	−16.2090			−0.953472
$290$	1.73919	−	3.36412i	0.102129	−	0.197548i
$291$		0			0
$292$	−12.2165	+	0.178336i	−0.714916	+	0.0104364i
$293$	−11.1453	+	19.3041i	−0.651113	+	1.12776i	0.331741	+	0.943371i	$0.392364\pi$
$293$	−11.1453	+	19.3041i	−0.651113	+	1.12776i	−0.982853	+	0.184390i	$0.940969\pi$
$294$		0			0
$295$	3.49532	+	3.23176i	0.203506	+	0.188160i
$296$	−23.4930	−	22.4861i	−1.36550	−	1.30698i
$297$		0			0
$298$	3.14763	+	11.4133i	0.182337	+	0.661153i
$299$	−16.0032	−	27.7184i	−0.925490	−	1.60300i
$300$		0			0
$301$	−13.8448	+	23.9798i	−0.797999	+	1.38217i
$302$	−22.4429	−	5.83834i	−1.29144	−	0.335959i
$303$		0			0
$304$	−0.354408	−	12.1363i	−0.0203267	−	0.696066i
$305$	8.17078	−	2.53611i	0.467857	−	0.145217i
$306$		0			0
$307$	−0.415414			−0.0237089			−0.0118545	−	0.999930i	$-0.503773\pi$
$307$	−0.415414			−0.0237089			−0.0118545	+	0.999930i	$0.503773\pi$
$308$	−13.6578	−	7.62170i	−0.778224	−	0.434287i
$309$		0			0
$310$	−0.748373	+	0.0347931i	−0.0425047	+	0.00197611i
$311$	0.284562	−	0.492876i	0.0161360	−	0.0279484i	−0.857845	−	0.513909i	$-0.828197\pi$
$311$	0.284562	−	0.492876i	0.0161360	−	0.0279484i	0.873981	+	0.485961i	$0.161530\pi$
$312$		0			0
$313$	24.3028	−	14.0312i	1.37367	−	0.793091i	0.382285	−	0.924044i	$-0.375137\pi$
$313$	24.3028	−	14.0312i	1.37367	−	0.793091i	0.991388	+	0.130954i	$0.0418039\pi$
$314$	−4.02762	−	14.6041i	−0.227292	−	0.824156i
$315$		0			0
$316$	10.5932	+	17.7447i	0.595917	+	0.998219i
$317$	−6.63676	−	11.4952i	−0.372758	−	0.645635i	0.617231	−	0.786782i	$-0.288254\pi$
$317$	−6.63676	−	11.4952i	−0.372758	−	0.645635i	−0.989989	+	0.141147i	$0.954921\pi$
$318$		0			0
$319$	2.44664	+	1.41257i	0.136986	+	0.0790887i
$320$	−17.6032	−	3.18232i	−0.984049	−	0.177897i
$321$		0			0
$322$	23.9370	−	24.2890i	1.33396	−	1.35357i
$323$		−	2.69956i		−	0.150208i
$324$		0			0
$325$	−12.4572	−	18.1338i	−0.690999	−	1.00588i
$326$	−1.34555	−	1.32605i	−0.0745231	−	0.0734431i
$327$		0			0
$328$	−7.68850	+	2.24165i	−0.424526	+	0.123774i
$329$	21.7398	+	12.5515i	1.19855	+	0.691985i
$330$		0			0
$331$	7.43989	−	4.29542i	0.408933	−	0.236098i	−0.281398	−	0.959591i	$-0.590798\pi$
$331$	7.43989	−	4.29542i	0.408933	−	0.236098i	0.690331	+	0.723493i	$0.257465\pi$
$332$	−2.66471	−	4.46364i	−0.146245	−	0.244974i
$333$		0			0
$334$	−2.69583	−	9.77502i	−0.147509	−	0.534865i
$335$	10.4170	+	9.63150i	0.569141	+	0.526225i
$336$		0			0
$337$	−0.914017	−	0.527708i	−0.0497897	−	0.0287461i	0.474899	−	0.880041i	$-0.342485\pi$
$337$	−0.914017	−	0.527708i	−0.0497897	−	0.0287461i	−0.524688	+	0.851294i	$0.675818\pi$
$338$	2.26469	−	8.70561i	0.123183	−	0.473523i
$339$		0			0
$340$	−3.89161	−	0.821507i	−0.211052	−	0.0445525i
$341$		−	0.558884i		−	0.0302652i
$342$		0			0
$343$	−9.98036			−0.538889
$344$	−22.9485	−	5.61355i	−1.23730	−	0.302662i
$345$		0			0
$346$	−0.916922	+	3.52470i	−0.0492940	+	0.189489i
$347$	−5.97844	−	3.45165i	−0.320939	−	0.185294i	0.330872	−	0.943676i	$-0.392657\pi$
$347$	−5.97844	−	3.45165i	−0.320939	−	0.185294i	−0.651811	+	0.758381i	$0.725991\pi$
$348$		0			0
$349$	−15.5145	−	26.8719i	−0.830473	−	1.43842i	−0.897663	−	0.440682i	$-0.854737\pi$
$349$	−15.5145	−	26.8719i	−0.830473	−	1.43842i	0.0671899	−	0.997740i	$-0.478597\pi$
$350$	15.0970	−	17.9318i	0.806968	−	0.958493i
$351$		0			0
$352$	2.98128	−	13.0074i	0.158903	−	0.693299i
$353$	7.67847	+	13.2995i	0.408684	+	0.707861i	0.994743	−	0.102408i	$-0.0326546\pi$
$353$	7.67847	+	13.2995i	0.408684	+	0.707861i	−0.586059	+	0.810269i	$0.699321\pi$
$354$		0			0
$355$	5.78876	−	25.5695i	0.307235	−	1.35709i
$356$	−9.36161	+	0.136661i	−0.496164	+	0.00724301i
$357$		0			0
$358$	10.2588	+	10.1101i	0.542194	+	0.534337i
$359$	8.51196			0.449244			0.224622	−	0.974446i	$-0.427885\pi$
$359$	8.51196			0.449244			0.224622	+	0.974446i	$0.427885\pi$
$360$		0			0
$361$	9.78650			0.515079
$362$	−4.20573	−	4.14478i	−0.221048	−	0.217845i
$363$		0			0
$364$	29.1696	−	0.425818i	1.52890	−	0.0223189i
$365$	13.3227	+	3.01617i	0.697344	+	0.157874i
$366$		0			0
$367$	−0.646542	−	1.11984i	−0.0337492	−	0.0584553i	0.848657	−	0.528943i	$-0.177411\pi$
$367$	−0.646542	−	1.11984i	−0.0337492	−	0.0584553i	−0.882407	+	0.470488i	$0.844078\pi$
$368$	25.6120	+	13.8064i	1.33512	+	0.719708i
$369$		0			0
$370$	19.6219	+	30.6090i	1.02009	+	1.59129i
$371$	−1.27969	−	2.21648i	−0.0664381	−	0.115074i
$372$		0			0
$373$	−14.1837	−	8.18898i	−0.734406	−	0.424010i	0.0856259	−	0.996327i	$-0.472711\pi$
$373$	−14.1837	−	8.18898i	−0.734406	−	0.424010i	−0.820032	+	0.572318i	$0.806044\pi$
$374$	0.747002	−	2.87152i	0.0386265	−	0.148483i
$375$		0			0
$376$	−5.08917	+	20.8048i	−0.262454	+	1.07293i
$377$	−5.26946			−0.271391
$378$		0			0
$379$		−	11.7940i		−	0.605818i	−0.953020	−	0.302909i	$-0.902042\pi$
$379$		−	11.7940i		−	0.605818i	0.953020	−	0.302909i	$-0.0979578\pi$
$380$	−2.80377	+	13.2819i	−0.143830	+	0.681347i
$381$		0			0
$382$	8.91198	−	34.2582i	0.455977	−	1.75280i
$383$	9.75933	+	5.63455i	0.498678	+	0.287912i	0.728168	−	0.685399i	$-0.240372\pi$
$383$	9.75933	+	5.63455i	0.498678	+	0.287912i	−0.229489	+	0.973311i	$0.573706\pi$
$384$		0			0
$385$	12.8395	+	11.8713i	0.654361	+	0.605019i
$386$	7.11268	+	25.7905i	0.362026	+	1.31270i
$387$		0			0
$388$	−6.32944	−	10.6024i	−0.321328	−	0.538257i
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.872360	−	0.488864i	$-0.837411\pi$
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.0128115	+	0.999918i	$0.504078\pi$
$390$		0			0
$391$	5.60259	+	3.23466i	0.283335	+	0.163584i
$392$	3.15833	+	10.8326i	0.159520	+	0.547127i
$393$		0			0
$394$	5.29239	+	5.21569i	0.266627	+	0.262763i
$395$	−6.84932	−	22.0670i	−0.344627	−	1.11031i
$396$		0			0
$397$			5.11859i			0.256895i	0.991716	+	0.128447i	$0.0409993\pi$
$397$			5.11859i			0.256895i	−0.991716	+	0.128447i	$0.959001\pi$
$398$	18.7106	−	18.9858i	0.937879	−	0.951670i
$399$		0			0
$400$	18.2936	+	8.08366i	0.914678	+	0.404183i
$401$	−9.58291	−	5.53269i	−0.478548	−	0.276290i	0.241263	−	0.970460i	$-0.422438\pi$
$401$	−9.58291	−	5.53269i	−0.478548	−	0.276290i	−0.719811	+	0.694170i	$0.755772\pi$
$402$		0			0
$403$	0.521215	+	0.902771i	0.0259636	+	0.0449702i
$404$	7.95892	+	13.3320i	0.395971	+	0.663291i
$405$		0			0
$406$	−1.49267	−	5.41238i	−0.0740798	−	0.268612i
$407$	−23.4893	+	13.5615i	−1.16432	+	0.672221i
$408$		0			0
$409$	−8.08315	+	14.0004i	−0.399686	+	0.692276i	−0.993687	−	0.112188i	$-0.964214\pi$
$409$	−8.08315	+	14.0004i	−0.399686	+	0.692276i	0.594001	+	0.804464i	$0.297548\pi$
$410$	8.94425	−	0.415833i	0.441725	−	0.0205365i
$411$		0			0
$412$	22.9846	+	12.8265i	1.13237	+	0.631917i
$413$	7.05742			0.347273
$414$		0			0
$415$	1.72293	+	5.55090i	0.0845753	+	0.272483i
$416$	7.31504	+	23.7914i	0.358650	+	1.16647i
$417$		0			0
$418$	−9.80037	−	2.54949i	−0.479352	−	0.124699i
$419$	−3.65564	+	6.33176i	−0.178590	+	0.309327i	−0.941398	−	0.337298i	$-0.890487\pi$
$419$	−3.65564	+	6.33176i	−0.178590	+	0.309327i	0.762808	+	0.646625i	$0.223820\pi$
$420$		0			0
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	0.956992	+	0.290114i	$0.0936932\pi$
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	−0.227250	+	0.973836i	$0.572973\pi$
$422$	1.71959	+	6.23521i	0.0837083	+	0.303525i
$423$		0			0
$424$	1.50993	−	1.57755i	0.0733288	−	0.0766124i
$425$	4.01323	+	1.91530i	0.194670	+	0.0929056i
$426$		0			0
$427$	6.34172	−	10.9842i	0.306897	−	0.531562i
$428$	0.504295	−	0.00736171i	0.0243760	−	0.000355842i
$429$		0			0
$430$	23.4636	+	12.1303i	1.13152	+	0.584973i
$431$	30.7505			1.48120			0.740599	−	0.671947i	$-0.234542\pi$
$431$	30.7505			1.48120			0.740599	+	0.671947i	$0.234542\pi$
$432$		0			0
$433$			29.3734i			1.41160i	0.708413	+	0.705798i	$0.249411\pi$
$433$			29.3734i			1.41160i	−0.708413	+	0.705798i	$0.750589\pi$
$434$	−0.779614	+	0.791078i	−0.0374227	+	0.0379730i
$435$		0			0
$436$	0.0134016	+	0.918039i	0.000641818	+	0.0439661i
$437$	11.0398	−	19.1214i	0.528103	−	0.914701i
$438$		0			0
$439$	6.77418	−	3.91108i	0.323314	−	0.186665i	−0.329555	−	0.944136i	$-0.606899\pi$
$439$	6.77418	−	3.91108i	0.323314	−	0.186665i	0.652869	+	0.757471i	$0.273565\pi$
$440$	−6.65762	+	13.3521i	−0.317390	+	0.636535i
$441$		0			0
$442$	1.47134	+	5.33505i	0.0699844	+	0.253763i
$443$	−23.1263	+	13.3520i	−1.09876	+	0.634371i	−0.935896	−	0.352277i	$-0.885408\pi$
$443$	−23.1263	+	13.3520i	−1.09876	+	0.634371i	−0.162867	+	0.986648i	$0.552074\pi$
$444$		0			0
$445$	10.2093	+	2.31132i	0.483969	+	0.109567i
$446$	8.45731	−	32.5104i	0.400465	−	1.53941i
$447$		0			0
$448$	−22.3646	+	14.2528i	−1.05663	+	0.673381i
$449$		−	23.8441i		−	1.12527i	−0.826704	−	0.562637i	$-0.809787\pi$
$449$		−	23.8441i		−	1.12527i	0.826704	−	0.562637i	$-0.190213\pi$
$450$		0			0
$451$			6.67955i			0.314528i
$452$	30.4428	+	16.9886i	1.43191	+	0.799076i
$453$		0			0
$454$	−38.1272	−	9.91849i	−1.78940	−	0.465498i
$455$	−31.8110	−	7.20178i	−1.49132	−	0.337625i
$456$		0			0
$457$	13.6451	−	7.87798i	0.638289	−	0.368516i	−0.145666	−	0.989334i	$-0.546532\pi$
$457$	13.6451	−	7.87798i	0.638289	−	0.368516i	0.783955	+	0.620817i	$0.213199\pi$
$458$	−22.7944	+	6.28641i	−1.06511	+	0.293745i
$459$		0			0
$460$	−24.2053	−	21.7334i	−1.12858	−	1.01333i
$461$	−9.24515	+	5.33769i	−0.430590	+	0.248601i	−0.699598	−	0.714537i	$-0.746637\pi$
$461$	−9.24515	+	5.33769i	−0.430590	+	0.248601i	0.269008	+	0.963138i	$0.413304\pi$
$462$		0			0
$463$	−3.17644	+	5.50175i	−0.147622	+	0.255688i	−0.930348	−	0.366678i	$-0.880495\pi$
$463$	−3.17644	+	5.50175i	−0.147622	+	0.255688i	0.782726	+	0.622366i	$0.213828\pi$
$464$	4.07687	−	2.51524i	0.189264	−	0.116767i
$465$		0			0
$466$	−1.69160	−	1.66708i	−0.0783617	−	0.0772261i
$467$		−	7.76191i		−	0.359179i	−0.983742	−	0.179589i	$-0.942523\pi$
$467$		−	7.76191i		−	0.359179i	0.983742	−	0.179589i	$-0.0574769\pi$
$468$		0			0
$469$	21.0330			0.971213
$470$	10.9971	−	21.2718i	0.507259	−	0.981194i
$471$		0			0
$472$	1.68545	+	5.78081i	0.0775790	+	0.266083i
$473$	−9.85221	+	17.0645i	−0.453005	+	0.784628i
$474$		0			0
$475$	6.53683	−	13.6970i	0.299930	−	0.628461i
$476$	−5.06298	+	3.02249i	−0.232061	+	0.138536i
$477$		0			0
$478$	14.7534	−	4.06880i	0.674805	−	0.186103i
$479$	3.56565	+	6.17588i	0.162919	+	0.282183i	0.935914	−	0.352228i	$-0.114576\pi$
$479$	3.56565	+	6.17588i	0.162919	+	0.282183i	−0.772996	+	0.634411i	$0.781243\pi$
$480$		0			0
$481$	25.2950	−	43.8122i	1.15335	−	1.99767i
$482$	−3.88558	+	14.9364i	−0.176983	+	0.680333i
$483$		0			0
$484$	9.49194	+	5.29697i	0.431452	+	0.240771i
$485$	4.09245	+	13.1850i	0.185829	+	0.598699i
$486$		0			0
$487$	−15.1089			−0.684649			−0.342325	−	0.939582i	$-0.611214\pi$
$487$	−15.1089			−0.684649			−0.342325	+	0.939582i	$0.611214\pi$
$488$	10.5118	+	2.57134i	0.475846	+	0.116399i
$489$		0			0
$490$	−0.585879	−	12.6018i	−0.0264673	−	0.569292i
$491$	14.7215	−	25.4984i	0.664372	−	1.15073i	−0.315083	−	0.949064i	$-0.602032\pi$
$491$	14.7215	−	25.4984i	0.664372	−	1.15073i	0.979455	−	0.201662i	$-0.0646342\pi$
$492$		0			0
$493$	0.922396	−	0.532546i	0.0415426	−	0.0239847i
$494$	18.2083	−	5.02162i	0.819230	−	0.225933i
$495$		0			0
$496$	−0.834168	−	0.449666i	−0.0374552	−	0.0201906i
$497$	−19.4333	−	33.6595i	−0.871705	−	1.50984i
$498$		0			0
$499$	18.0795	+	10.4382i	0.809351	+	0.467279i	0.846730	−	0.532022i	$-0.178568\pi$
$499$	18.0795	+	10.4382i	0.809351	+	0.467279i	−0.0373795	+	0.999301i	$0.511901\pi$
$500$	−17.7559	−	13.5914i	−0.794069	−	0.607828i
$501$		0			0
$502$	−5.09444	−	5.02061i	−0.227376	−	0.224081i
$503$			22.6713i			1.01086i	0.862867	+	0.505431i	$0.168667\pi$
$503$			22.6713i			1.01086i	−0.862867	+	0.505431i	$0.831333\pi$
$504$		0			0
$505$	−5.14603	−	16.5794i	−0.228995	−	0.737773i
$506$	17.0341	−	17.2846i	0.757257	−	0.768392i
$507$		0			0
$508$	0.308470	+	21.1310i	0.0136862	+	0.937535i
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.921033	−	0.389484i	$-0.127347\pi$
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.123213	+	0.992380i	$0.460680\pi$
$510$		0			0
$511$	17.5380	−	10.1255i	0.775834	−	0.447928i
$512$	−17.0157	−	14.9153i	−0.751996	−	0.659168i
$513$		0			0
$514$	−18.2560	+	5.03476i	−0.805236	+	0.222074i
$515$	−21.6075	−	19.9782i	−0.952141	−	0.880345i
$516$		0			0
$517$	15.4705	+	8.93188i	0.680390	+	0.392824i
$518$	52.1658	+	13.5705i	2.29204	+	0.596254i
$519$		0			0
$520$	−1.69802	−	27.7767i	−0.0744631	−	1.21809i
$521$			2.18176i			0.0955847i	0.998857	+	0.0477924i	$0.0152186\pi$
$521$			2.18176i			0.0955847i	−0.998857	+	0.0477924i	$0.984781\pi$
$522$		0			0
$523$	−28.8185			−1.26014			−0.630071	−	0.776537i	$-0.716974\pi$
$523$	−28.8185			−1.26014			−0.630071	+	0.776537i	$0.716974\pi$
$524$	28.3940	+	15.8452i	1.24040	+	0.692203i
$525$		0			0
$526$	−14.9065	−	3.87779i	−0.649953	−	0.169080i
$527$	−0.182473	−	0.105351i	−0.00794865	−	0.00458916i
$528$		0			0
$529$	14.9560	+	25.9046i	0.650261	+	1.12629i
$530$	−2.05539	+	1.31760i	−0.0892802	+	0.0572330i
$531$		0			0
$532$	10.3156	+	17.2797i	0.447240	+	0.749171i
$533$	−6.22935	−	10.7896i	−0.269823	−	0.467348i
$534$		0			0
$535$	−0.549962	−	0.124507i	−0.0237769	−	0.00538292i
$536$	5.02308	+	17.2283i	0.216964	+	0.744151i
$537$		0			0
$538$	−21.3445	+	21.6584i	−0.920227	+	0.933759i
$539$	9.41102			0.405361
$540$		0			0
$541$	3.32257			0.142848			0.0714242	−	0.997446i	$-0.477246\pi$
$541$	3.32257			0.142848			0.0714242	+	0.997446i	$0.477246\pi$
$542$	−18.8058	+	19.0823i	−0.807777	+	0.819655i
$543$		0			0
$544$	−3.68489	−	3.42531i	−0.157989	−	0.146859i
$545$	0.226658	−	1.00117i	0.00970897	−	0.0428855i
$546$		0			0
$547$	−13.8697	−	24.0231i	−0.593027	−	1.02715i	−0.993822	−	0.110986i	$-0.964599\pi$
$547$	−13.8697	−	24.0231i	−0.593027	−	1.02715i	0.400795	−	0.916168i	$-0.368734\pi$
$548$	−22.6538	+	13.5238i	−0.967721	+	0.577710i
$549$		0			0
$550$	10.7433	−	12.7606i	0.458097	−	0.544114i
$551$	−1.81756	−	3.14810i	−0.0774305	−	0.134114i
$552$		0			0
$553$	−29.6652	−	17.1272i	−1.26149	−	0.728323i
$554$	25.5417	+	6.64447i	1.08516	+	0.282296i
$555$		0			0
$556$	6.31943	−	11.3241i	0.268003	−	0.480251i
$557$	30.0401			1.27284			0.636419	−	0.771344i	$-0.280415\pi$
$557$	30.0401			1.27284			0.636419	+	0.771344i	$0.280415\pi$
$558$		0			0
$559$		−	36.7527i		−	1.55447i
$560$	28.0491	−	9.61231i	1.18529	−	0.406194i
$561$		0			0
$562$	−9.24028	−	2.40378i	−0.389778	−	0.101398i
$563$	1.52959	+	0.883109i	0.0644645	+	0.0372186i	0.531886	−	0.846816i	$-0.321484\pi$
$563$	1.52959	+	0.883109i	0.0644645	+	0.0372186i	−0.467421	+	0.884035i	$0.654817\pi$
$564$		0			0
$565$	−28.6189	−	26.4609i	−1.20401	−	1.11322i
$566$	−7.18435	+	1.98135i	−0.301981	+	0.0832824i
$567$		0			0
$568$	22.9298	−	23.9566i	0.962115	−	1.00520i
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.986999	−	0.160726i	$-0.948616\pi$
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.354306	+	0.935129i	$0.615283\pi$
$570$		0			0
$571$	−26.5164	−	15.3092i	−1.10968	−	0.640672i	−0.170930	−	0.985283i	$-0.554677\pi$
$571$	−26.5164	−	15.3092i	−1.10968	−	0.640672i	−0.938745	+	0.344612i	$0.888011\pi$
$572$	20.7577	−	0.303021i	0.867922	−	0.0126699i
$573$		0			0
$574$	9.31764	−	9.45465i	0.388911	−	0.394629i
$575$	20.5938	+	29.9783i	0.858819	+	1.25018i
$576$		0			0
$577$			23.6405i			0.984168i	0.870548	+	0.492084i	$0.163765\pi$
$577$			23.6405i			0.984168i	−0.870548	+	0.492084i	$0.836235\pi$
$578$	16.3269	+	16.0903i	0.679109	+	0.669268i
$579$		0			0
$580$	−5.09131	+	1.66213i	−0.211405	+	0.0690163i
$581$	7.46221	+	4.30831i	0.309585	+	0.178739i
$582$		0			0
$583$	−0.910652	−	1.57730i	−0.0377154	−	0.0653249i
$584$	12.4824	+	11.9474i	0.516523	+	0.494385i
$585$		0			0
$586$	30.3890	−	8.38091i	1.25536	−	0.346212i
$587$	0.0513568	−	0.0296509i	0.00211972	−	0.00122382i	−0.498940	−	0.866637i	$-0.666277\pi$
$587$	0.0513568	−	0.0296509i	0.00211972	−	0.00122382i	0.501059	+	0.865413i	$0.332944\pi$
$588$		0			0
$589$	−0.359558	+	0.622773i	−0.0148153	+	0.0256609i
$590$	−0.312655	−	6.72498i	−0.0128718	−	0.276863i
$591$		0			0
$592$	1.34244	+	45.9705i	0.0551741	+	1.88938i
$593$	−44.6245			−1.83251			−0.916255	−	0.400596i	$-0.868803\pi$
$593$	−44.6245			−1.83251			−0.916255	+	0.400596i	$0.868803\pi$
$594$		0			0
$595$	6.29622	−	1.95427i	0.258120	−	0.0801171i
$596$	8.15914	−	14.6208i	0.334211	−	0.598893i
$597$		0			0
$598$	−11.3958	+	43.8059i	−0.466007	+	1.79136i
$599$	−11.5001	+	19.9187i	−0.469881	+	0.813857i	−0.999407	−	0.0344362i	$-0.989036\pi$
$599$	−11.5001	+	19.9187i	−0.469881	+	0.813857i	0.529526	+	0.848294i	$0.322370\pi$
$600$		0			0
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	0.885344	−	0.464936i	$-0.153923\pi$
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	−0.845319	+	0.534262i	$0.820589\pi$
$602$	37.7496	−	10.4109i	1.53856	−	0.424315i
$603$		0			0
$604$	16.8105	+	28.1593i	0.684011	+	1.14579i
$605$	−8.92325	−	8.25040i	−0.362782	−	0.335426i
$606$		0			0
$607$	10.1049	−	17.5023i	0.410146	−	0.710394i	−0.584759	−	0.811207i	$-0.698811\pi$
$607$	10.1049	−	17.5023i	0.410146	−	0.710394i	0.994905	+	0.100813i	$0.0321443\pi$
$608$	−11.6904	+	12.5764i	−0.474110	+	0.510040i
$609$		0			0
$610$	−10.7477	−	5.55638i	−0.435163	−	0.224971i
$611$	−33.3195			−1.34796
$612$		0			0
$613$		−	24.8672i		−	1.00438i	−0.864758	−	0.502189i	$-0.832528\pi$
$613$		−	24.8672i		−	1.00438i	0.864758	−	0.502189i	$-0.167472\pi$
$614$	0.418434	+	0.412371i	0.0168866	+	0.0166419i
$615$		0			0
$616$	6.19121	+	21.2349i	0.249451	+	0.855577i
$617$	−16.3707	+	28.3549i	−0.659059	+	1.14152i	0.321800	+	0.946808i	$0.395712\pi$
$617$	−16.3707	+	28.3549i	−0.659059	+	1.14152i	−0.980860	+	0.194717i	$0.937621\pi$
$618$		0			0
$619$	11.9754	−	6.91400i	0.481332	−	0.277897i	−0.239640	−	0.970862i	$-0.577029\pi$
$619$	11.9754	−	6.91400i	0.481332	−	0.277897i	0.720971	+	0.692965i	$0.243696\pi$
$620$	0.788353	+	0.707845i	0.0316610	+	0.0284277i
$621$		0			0
$622$	−0.775897	+	0.213982i	−0.0311106	+	0.00857991i
$623$	13.4395	−	7.75930i	0.538442	−	0.310870i
$624$		0			0
$625$	15.7244	+	19.4356i	0.628978	+	0.777423i
$626$	−38.4079	−	9.99151i	−1.53509	−	0.399341i
$627$		0			0
$628$	−10.4402	+	18.7084i	−0.416609	+	0.746546i
$629$			10.2255i			0.407719i
$630$		0			0
$631$			0.298908i			0.0118994i	0.999982	+	0.00594968i	$0.00189385\pi$
$631$			0.298908i			0.0118994i	−0.999982	+	0.00594968i	$0.998106\pi$
$632$	6.94447	−	28.3894i	0.276236	−	1.12927i
$633$		0			0
$634$	−4.72598	+	18.1669i	−0.187693	+	0.721501i
$635$	5.21710	−	23.0445i	0.207034	−	0.914492i
$636$		0			0
$637$	−15.2017	+	8.77672i	−0.602314	+	0.347746i
$638$	−1.06221	−	3.85156i	−0.0420534	−	0.152485i
$639$		0			0
$640$	14.5722	+	20.6797i	0.576017	+	0.817438i
$641$	−12.2453	+	7.06982i	−0.483660	+	0.279241i	−0.721940	−	0.691955i	$-0.756750\pi$
$641$	−12.2453	+	7.06982i	−0.483660	+	0.279241i	0.238281	+	0.971196i	$0.423416\pi$
$642$		0			0
$643$	−18.2808	+	31.6633i	−0.720925	+	1.24868i	0.239704	+	0.970846i	$0.422950\pi$
$643$	−18.2808	+	31.6633i	−0.720925	+	1.24868i	−0.960629	+	0.277833i	$0.910384\pi$
$644$	−48.2222	+	0.703948i	−1.90022	+	0.0277394i
$645$		0			0
$646$	−2.67979	+	2.71919i	−0.105435	+	0.106985i
$647$		−	25.4645i		−	1.00111i	−0.865704	−	0.500556i	$-0.833129\pi$
$647$		−	25.4645i		−	1.00111i	0.865704	−	0.500556i	$-0.166871\pi$
$648$		0			0
$649$	5.02220			0.197139
$650$	−5.45327	+	30.6316i	−0.213895	+	1.20147i
$651$		0			0
$652$	0.0389969	+	2.67139i	0.00152724	+	0.104620i
$653$	11.2123	−	19.4203i	0.438772	−	0.759976i	−0.558823	−	0.829287i	$-0.688747\pi$
$653$	11.2123	−	19.4203i	0.438772	−	0.759976i	0.997595	+	0.0693112i	$0.0220801\pi$
$654$		0			0
$655$	−26.6929	−	24.6801i	−1.04298	−	0.964330i
$656$	9.96964	+	5.37423i	0.389249	+	0.209828i
$657$		0			0
$658$	−9.43834	−	34.2233i	−0.367945	−	1.33416i
$659$	−3.28193	−	5.68446i	−0.127846	−	0.221435i	0.794996	−	0.606615i	$-0.207473\pi$
$659$	−3.28193	−	5.68446i	−0.127846	−	0.221435i	−0.922842	+	0.385179i	$0.874140\pi$
$660$		0			0
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	−0.989175	−	0.146741i	$-0.953122\pi$
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	0.621669	+	0.783280i	$0.286455\pi$
$662$	−11.7579	−	3.05873i	−0.456986	−	0.118881i
$663$		0			0
$664$	−1.74687	+	7.14129i	−0.0677915	+	0.277136i
$665$	−6.66983	−	21.4887i	−0.258645	−	0.833297i
$666$		0			0
$667$	8.71129			0.337303
$668$	−6.98799	+	12.5222i	−0.270373	+	0.484498i
$669$		0			0
$670$	−0.931795	−	20.0422i	−0.0359984	−	0.774299i
$671$	4.51290	−	7.81657i	0.174219	−	0.301755i
$672$		0			0
$673$	27.1258	−	15.6611i	1.04562	−	0.603690i	0.124201	−	0.992257i	$-0.460363\pi$
$673$	27.1258	−	15.6611i	1.04562	−	0.603690i	0.921420	+	0.388567i	$0.127030\pi$
$674$	0.396821	+	1.43887i	0.0152850	+	0.0554231i
$675$		0			0
$676$	−10.9230	+	6.52081i	−0.420115	+	0.250800i
$677$	20.4922	+	35.4936i	0.787580	+	1.36413i	0.927446	+	0.373958i	$0.122000\pi$
$677$	20.4922	+	35.4936i	0.787580	+	1.36413i	−0.139866	+	0.990171i	$0.544667\pi$
$678$		0			0
$679$	17.7249	+	10.2335i	0.680219	+	0.392724i
$680$	3.10442	+	4.69058i	0.119049	+	0.179876i
$681$		0			0
$682$	−0.554790	+	0.562948i	−0.0212440	+	0.0215564i
$683$			42.0703i			1.60978i	0.593427	+	0.804888i	$0.297775\pi$
$683$			42.0703i			1.60978i	−0.593427	+	0.804888i	$0.702225\pi$
$684$		0			0
$685$	28.1718	−	8.74417i	1.07639	−	0.334097i
$686$	10.0529	+	9.90726i	0.383823	+	0.378261i
$687$		0			0
$688$	17.5430	+	28.4348i	0.668820	+	1.08407i
$689$	2.94198	+	1.69855i	0.112080	+	0.0647096i
$690$		0			0
$691$	−30.3277	+	17.5097i	−1.15372	+	0.666101i	−0.949791	−	0.312885i	$-0.898705\pi$
$691$	−30.3277	+	17.5097i	−1.15372	+	0.666101i	−0.203930	+	0.978986i	$0.565371\pi$
$692$	4.42247	−	2.64012i	0.168117	−	0.100362i
$693$		0			0
$694$	2.59554	+	9.41140i	0.0985255	+	0.357252i
$695$	−9.84295	+	10.6457i	−0.373364	+	0.403814i
$696$		0			0
$697$	2.18084	+	1.25911i	0.0826054	+	0.0476922i
$698$	−11.0478	+	42.4682i	−0.418164	+	1.60745i
$699$		0			0
$700$	−33.0072	+	3.07576i	−1.24755	+	0.116253i
$701$		−	41.5315i		−	1.56862i	−0.620366	−	0.784312i	$-0.713016\pi$
$701$		−	41.5315i		−	1.56862i	0.620366	−	0.784312i	$-0.286984\pi$
$702$		0			0
$703$	34.8993			1.31625
$704$	−15.9151	+	10.1426i	−0.599824	+	0.382263i
$705$		0			0
$706$	5.46777	−	21.0184i	0.205782	−	0.791039i
$707$	−22.2881	−	12.8680i	−0.838229	−	0.483952i
$708$		0			0
$709$	5.69139	+	9.85778i	0.213745	+	0.370217i	0.952883	−	0.303337i	$-0.0981006\pi$
$709$	5.69139	+	9.85778i	0.213745	+	0.370217i	−0.739139	+	0.673553i	$0.764767\pi$
$710$	−31.2131	+	20.0091i	−1.17141	+	0.750929i
$711$		0			0
$712$	9.56534	+	9.15538i	0.358476	+	0.343112i
$713$	−0.861656	−	1.49243i	−0.0322693	−	0.0558920i
$714$		0			0
$715$	−22.6374	−	5.12494i	−0.846590	−	0.191662i
$716$	−0.297322	−	20.3673i	−0.0111115	−	0.761162i
$717$		0			0
$718$	−8.57386	−	8.44961i	−0.319974	−	0.315337i
$719$	24.0599			0.897282			0.448641	−	0.893712i	$-0.351908\pi$
$719$	24.0599			0.897282			0.448641	+	0.893712i	$0.351908\pi$
$720$		0			0
$721$	−43.6278			−1.62478
$722$	−9.85767	−	9.71482i	−0.366864	−	0.361548i
$723$		0			0
$724$	0.121891	+	8.34985i	0.00453005	+	0.310320i
$725$	5.96956	−	0.468490i	0.221704	−	0.0173993i
$726$		0			0
$727$	2.85756	+	4.94944i	0.105981	+	0.183565i	0.914139	−	0.405402i	$-0.132868\pi$
$727$	2.85756	+	4.94944i	0.105981	+	0.183565i	−0.808158	+	0.588966i	$0.799535\pi$
$728$	−29.8044	−	28.5270i	−1.10462	−	1.05728i
$729$		0			0
$730$	−10.4255	−	16.2633i	−0.385867	−	0.601930i
$731$	3.71433	+	6.43341i	0.137380	+	0.237948i
$732$		0			0
$733$	−22.3900	−	12.9269i	−0.826994	−	0.477465i	0.0258286	−	0.999666i	$-0.491778\pi$
$733$	−22.3900	−	12.9269i	−0.826994	−	0.477465i	−0.852822	+	0.522201i	$0.825111\pi$
$734$	−0.460397	+	1.76979i	−0.0169936	+	0.0653242i
$735$		0			0
$736$	−12.0930	−	39.3312i	−0.445754	−	1.44977i
$737$	14.9675			0.551335
$738$		0			0
$739$			18.0774i			0.664989i	0.943105	+	0.332495i	$0.107890\pi$
$739$			18.0774i			0.664989i	−0.943105	+	0.332495i	$0.892110\pi$
$740$	10.6202	−	50.3098i	0.390408	−	1.84942i
$741$		0			0
$742$	−0.911255	+	3.50292i	−0.0334532	+	0.128596i
$743$	−15.5973	−	9.00512i	−0.572210	−	0.330366i	0.185821	−	0.982584i	$-0.440505\pi$
$743$	−15.5973	−	9.00512i	−0.572210	−	0.330366i	−0.758032	+	0.652218i	$0.773839\pi$
$744$		0			0
$745$	−12.7084	+	13.7449i	−0.465601	+	0.503573i
$746$	6.15788	+	22.3284i	0.225456	+	0.817500i
$747$		0			0
$748$	−3.60292	+	2.15087i	−0.131736	+	0.0786435i
$749$	−0.723965	+	0.417982i	−0.0264531	+	0.0152727i
$750$		0			0
$751$	35.2487	+	20.3509i	1.28624	+	0.742613i	0.977982	−	0.208689i	$-0.0669195\pi$
$751$	35.2487	+	20.3509i	1.28624	+	0.742613i	0.308262	+	0.951302i	$0.400253\pi$
$752$	25.7786	−	15.9042i	0.940049	−	0.579967i
$753$		0			0
$754$	5.30778	+	5.23086i	0.193298	+	0.190497i
$755$	−10.8693	−	35.0184i	−0.395573	−	1.27445i
$756$		0			0
$757$		−	35.4823i		−	1.28963i	−0.764340	−	0.644813i	$-0.776935\pi$
$757$		−	35.4823i		−	1.28963i	0.764340	−	0.644813i	$-0.223065\pi$
$758$	−11.7076	+	11.8798i	−0.425240	+	0.431493i
$759$		0			0
$760$	16.0088	−	10.5952i	0.580699	−	0.384330i
$761$	34.0009	+	19.6304i	1.23253	+	0.711602i	0.967557	−	0.252654i	$-0.0813033\pi$
$761$	34.0009	+	19.6304i	1.23253	+	0.711602i	0.264974	+	0.964256i	$0.414637\pi$
$762$		0			0
$763$	−0.760910	−	1.31794i	−0.0275468	−	0.0477125i
$764$	−42.9840	+	25.6606i	−1.55511	+	0.928367i
$765$		0			0
$766$	−4.23702	−	15.3634i	−0.153090	−	0.555101i
$767$	−8.11242	+	4.68371i	−0.292923	+	0.169119i
$768$		0			0
$769$	−3.27941	+	5.68011i	−0.118259	+	0.204830i	−0.919078	−	0.394076i	$-0.871065\pi$
$769$	−3.27941	+	5.68011i	−0.118259	+	0.204830i	0.800819	+	0.598906i	$0.204398\pi$
$770$	−1.14849	−	24.7031i	−0.0413886	−	0.890238i
$771$		0			0
$772$	18.4371	−	33.0386i	0.663567	−	1.18908i
$773$	34.2118			1.23051			0.615256	−	0.788327i	$-0.289053\pi$
$773$	34.2118			1.23051			0.615256	+	0.788327i	$0.289053\pi$
$774$		0			0
$775$	−0.670727	−	0.976374i	−0.0240932	−	0.0350724i
$776$	−4.14930	+	16.9626i	−0.148951	+	0.608922i
$777$		0			0
$778$	27.5910	+	7.17757i	0.989185	+	0.257328i
$779$	4.29729	−	7.44313i	0.153967	−	0.266678i
$780$		0			0
$781$	−13.8292	−	23.9528i	−0.494847	−	0.857099i
$782$	−2.43237	−	8.81973i	−0.0869813	−	0.315393i
$783$		0			0
$784$	7.57191	−	14.0465i	0.270425	−	0.501661i
$785$	16.2613	−	17.5875i	0.580392	−	0.627726i
$786$		0			0
$787$	8.68943	−	15.0505i	0.309745	−	0.536494i	−0.668562	−	0.743657i	$-0.733090\pi$
$787$	8.68943	−	15.0505i	0.309745	−	0.536494i	0.978306	+	0.207163i	$0.0664230\pi$
$788$	−0.153385	−	10.5072i	−0.00546411	−	0.374305i
$789$		0			0
$790$	−15.0062	+	29.0266i	−0.533898	+	1.03272i
$791$	−57.7846			−2.05458
$792$		0			0
$793$			16.8349i			0.597826i
$794$	5.08109	−	5.15581i	0.180321	−	0.182973i
$795$		0			0
$796$	−37.6934	+	0.550249i	−1.33601	+	0.0195030i
$797$	3.50633	−	6.07314i	0.124201	−	0.215122i	−0.797220	−	0.603689i	$-0.793697\pi$
$797$	3.50633	−	6.07314i	0.124201	−	0.215122i	0.921420	+	0.388568i	$0.127030\pi$
$798$		0			0
$799$	5.83244	−	3.36736i	0.206337	−	0.119129i
$800$	−10.4021	−	26.3020i	−0.367771	−	0.929916i
$801$		0			0
$802$	4.16042	+	15.0856i	0.146910	+	0.532692i
$803$	12.4804	−	7.20555i	0.440423	−	0.254278i
$804$		0			0
$805$	52.5889	+	11.9058i	1.85352	+	0.419623i
$806$	0.371153	−	1.42673i	0.0130733	−	0.0502545i
$807$		0			0
$808$	5.21752	−	21.3295i	0.183552	−	0.750371i
$809$		−	38.9234i		−	1.36847i	−0.729261	−	0.684236i	$-0.760136\pi$
$809$		−	38.9234i		−	1.36847i	0.729261	−	0.684236i	$-0.239864\pi$
$810$		0			0
$811$			35.7891i			1.25673i	0.777920	+	0.628363i	$0.216275\pi$
$811$			35.7891i			1.25673i	−0.777920	+	0.628363i	$0.783725\pi$
$812$	−3.86922	+	6.93347i	−0.135783	+	0.243317i
$813$		0			0
$814$	37.1223	+	9.65706i	1.30114	+	0.338480i
$815$	0.659548	−	2.91329i	0.0231030	−	0.102048i
$816$		0			0
$817$	21.9570	−	12.6769i	0.768177	−	0.443507i
$818$	22.0398	−	6.07829i	0.770604	−	0.212523i
$819$		0			0
$820$	−9.42208	−	8.45988i	−0.329033	−	0.295432i
$821$	27.8765	−	16.0945i	0.972895	−	0.561701i	0.0727775	−	0.997348i	$-0.476814\pi$
$821$	27.8765	−	16.0945i	0.972895	−	0.561701i	0.900118	+	0.435647i	$0.143480\pi$
$822$		0			0
$823$	8.65813	−	14.9963i	0.301804	−	0.522739i	−0.674741	−	0.738055i	$-0.735745\pi$
$823$	8.65813	−	14.9963i	0.301804	−	0.522739i	0.976545	+	0.215315i	$0.0690780\pi$
$824$	−10.4192	−	35.7360i	−0.362969	−	1.24492i
$825$		0			0
$826$	−7.10874	−	7.00572i	−0.247345	−	0.243760i
$827$			15.5363i			0.540249i	0.962825	+	0.270124i	$0.0870648\pi$
$827$			15.5363i			0.540249i	−0.962825	+	0.270124i	$0.912935\pi$
$828$		0			0
$829$	−27.4645			−0.953882			−0.476941	−	0.878935i	$-0.658254\pi$
$829$	−27.4645			−0.953882			−0.476941	+	0.878935i	$0.658254\pi$
$830$	3.77478	−	7.30157i	0.131025	−	0.253441i
$831$		0			0
$832$	16.2489	−	31.2259i	0.563330	−	1.08256i
$833$	1.77400	−	3.07266i	0.0614654	−	0.106461i
$834$		0			0
$835$	10.8843	−	11.7719i	0.376666	−	0.407385i
$836$	7.34082	+	12.2966i	0.253888	+	0.425287i
$837$		0			0
$838$	9.96761	−	2.74894i	0.344325	−	0.0949605i
$839$	6.91476	+	11.9767i	0.238724	+	0.413482i	0.960348	−	0.278803i	$-0.0899376\pi$
$839$	6.91476	+	11.9767i	0.238724	+	0.413482i	−0.721624	+	0.692285i	$0.756604\pi$
$840$		0			0
$841$	−13.7829	+	23.8727i	−0.475272	+	0.823196i
$842$	10.6622	−	40.9861i	0.367443	−	1.41247i
$843$		0			0
$844$	4.45744	−	7.98754i	0.153431	−	0.274943i
$845$	13.5836	−	4.21619i	0.467291	−	0.145041i
$846$		0			0
$847$	−18.0170			−0.619070
$848$	−3.08690	+	0.0901446i	−0.106005	+	0.00309558i
$849$		0			0
$850$	−2.14114	−	5.91306i	−0.0734406	−	0.202816i
$851$	−41.8169	+	72.4290i	−1.43346	+	2.48283i
$852$		0			0
$853$	−31.2866	+	18.0633i	−1.07123	+	0.618476i	−0.928518	−	0.371288i	$-0.878916\pi$
$853$	−31.2866	+	18.0633i	−1.07123	+	0.618476i	−0.142714	+	0.989764i	$0.545583\pi$
$854$	−17.2916	+	4.76879i	−0.591705	+	0.163185i
$855$		0			0
$856$	−0.515270	−	0.493186i	−0.0176116	−	0.0168568i
$857$	3.70493	+	6.41713i	0.126558	+	0.219205i	0.922341	−	0.386377i	$-0.126274\pi$
$857$	3.70493	+	6.41713i	0.126558	+	0.219205i	−0.795783	+	0.605582i	$0.792940\pi$
$858$		0			0
$859$	−35.7586	−	20.6452i	−1.22007	−	0.704407i	−0.255136	−	0.966905i	$-0.582120\pi$
$859$	−35.7586	−	20.6452i	−1.22007	−	0.704407i	−0.964932	+	0.262499i	$0.915453\pi$
$860$	−11.5928	−	35.5102i	−0.395312	−	1.21089i
$861$		0			0
$862$	−30.9741	−	30.5252i	−1.05498	−	1.03969i
$863$		−	46.7922i		−	1.59282i	−0.604754	−	0.796412i	$-0.706729\pi$
$863$		−	46.7922i		−	1.59282i	0.604754	−	0.796412i	$-0.293271\pi$
$864$		0			0
$865$	−5.49970	+	1.70704i	−0.186995	+	0.0580410i
$866$	29.1583	−	29.5870i	0.990838	−	1.00541i
$867$		0			0
$868$	1.57057	−	0.0229272i	0.0533085	−	0.000778199i
$869$	−21.1104	−	12.1881i	−0.716120	−	0.413452i
$870$		0			0
$871$	−24.1772	+	13.9587i	−0.819213	+	0.472973i
$872$	0.897815	−	0.938018i	0.0304039	−	0.0317653i
$873$		0			0
$874$	−30.1014	+	8.30157i	−1.01819	+	0.280805i
$875$	36.6777	+	5.33040i	1.23993	+	0.180200i
$876$		0			0
$877$	12.2576	+	7.07692i	0.413909	+	0.238970i	0.692468	−	0.721449i	$-0.256523\pi$
$877$	12.2576	+	7.07692i	0.413909	+	0.238970i	−0.278559	+	0.960419i	$0.589857\pi$
$878$	−10.7059	−	2.78504i	−0.361306	−	0.0939907i
$879$		0			0
$880$	19.9603	−	6.84032i	0.672862	−	0.230587i
$881$			13.5705i			0.457200i	0.973520	+	0.228600i	$0.0734148\pi$
$881$			13.5705i			0.457200i	−0.973520	+	0.228600i	$0.926585\pi$
$882$		0			0
$883$	−46.0353			−1.54921			−0.774606	−	0.632444i	$-0.782052\pi$
$883$	−46.0353			−1.54921			−0.774606	+	0.632444i	$0.782052\pi$
$884$	3.81393	−	6.83441i	0.128276	−	0.229866i
$885$		0			0
$886$	36.5486	+	9.50783i	1.22788	+	0.319422i
$887$	17.1621	+	9.90855i	0.576247	+	0.332696i	0.759641	−	0.650343i	$-0.225375\pi$
$887$	17.1621	+	9.90855i	0.576247	+	0.332696i	−0.183393	+	0.983040i	$0.558708\pi$
$888$		0			0
$889$	−17.5143	−	30.3356i	−0.587409	−	1.01742i
$890$	−7.98919	−	12.4627i	−0.267798	−	0.417750i
$891$		0			0
$892$	−40.7910	+	24.3514i	−1.36578	+	0.815346i
$893$	−11.4927	−	19.9059i	−0.384587	−	0.666125i
$894$		0			0
$895$	−5.02856	+	22.2117i	−0.168086	+	0.742454i
$896$	36.6756	+	7.84436i	1.22525	+	0.262062i
$897$		0			0
$898$	−23.6695	+	24.0175i	−0.789860	+	0.801475i
$899$	−0.283722			−0.00946265
$900$		0			0
$901$	−0.686641			−0.0228753
$902$	6.63062	−	6.72812i	0.220776	−	0.224022i
$903$		0			0
$904$	−13.8001	−	47.3320i	−0.458983	−	1.57424i
$905$	2.06153	−	9.10597i	0.0685274	−	0.302693i
$906$		0			0
$907$	24.4653	+	42.3752i	0.812358	+	1.40705i	0.911209	+	0.411943i	$0.135150\pi$
$907$	24.4653	+	42.3752i	0.812358	+	1.40705i	−0.0988513	+	0.995102i	$0.531517\pi$
$908$	28.5587	+	47.8386i	0.947752	+	1.58758i
$909$		0			0
$910$	24.8933	+	38.8321i	0.825205	+	1.28727i
$911$	−16.0978	−	27.8822i	−0.533343	−	0.923778i	−0.999242	−	0.0389396i	$-0.987602\pi$
$911$	−16.0978	−	27.8822i	−0.533343	−	0.923778i	0.465898	−	0.884838i	$-0.345731\pi$
$912$		0			0
$913$	5.31026	+	3.06588i	0.175744	+	0.101466i
$914$	−21.5646	−	5.60985i	−0.713292	−	0.185557i
$915$		0			0
$916$	29.2006	+	16.2953i	0.964814	+	0.538413i
$917$	−53.8956			−1.77979
$918$		0			0
$919$			37.8553i			1.24873i	0.781133	+	0.624365i	$0.214642\pi$
$919$			37.8553i			1.24873i	−0.781133	+	0.624365i	$0.785358\pi$
$920$	2.80711	+	45.9195i	0.0925477	+	1.51392i
$921$		0			0
$922$	14.6110	+	3.80093i	0.481187	+	0.125177i
$923$	44.6768	+	25.7942i	1.47056	+	0.849026i
$924$		0			0
$925$	−24.7605	+	51.8820i	−0.814121	+	1.70587i
$926$	8.66098	−	2.38859i	0.284618	−	0.0784939i
$927$		0			0
$928$	−6.60333	−	1.51347i	−0.216765	−	0.0496822i
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	−0.717998	−	0.696045i	$-0.754941\pi$
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	0.243794	+	0.969827i	$0.421608\pi$
$930$		0			0
$931$	−10.4868	−	6.05458i	−0.343693	−	0.198431i
$932$	0.0490261	+	3.35841i	0.00160590	+	0.110008i
$933$		0			0
$934$	−7.70506	+	7.81836i	−0.252117	+	0.255824i
$935$	4.48052	−	1.39070i	0.146529	−	0.0454806i
$936$		0			0
$937$		−	41.7514i		−	1.36396i	−0.731372	−	0.681979i	$-0.761120\pi$
$937$		−	41.7514i		−	1.36396i	0.731372	−	0.681979i	$-0.238880\pi$
$938$	−21.1859	−	20.8789i	−0.691745	−	0.681721i
$939$		0			0
$940$	−32.1931	+	10.5099i	−1.05002	+	0.342795i
$941$	−9.78882	−	5.65158i	−0.319106	−	0.184236i	0.331888	−	0.943319i	$-0.392314\pi$
$941$	−9.78882	−	5.65158i	−0.319106	−	0.184236i	−0.650994	+	0.759083i	$0.725648\pi$
$942$		0			0
$943$	10.2982	+	17.8369i	0.335354	+	0.580851i
$944$	4.04076	−	7.49595i	0.131516	−	0.243972i
$945$		0			0
$946$	26.8634	−	7.40858i	0.873404	−	0.240874i
$947$	4.45025	−	2.56935i	0.144614	−	0.0834928i	−0.425947	−	0.904748i	$-0.640059\pi$
$947$	4.45025	−	2.56935i	0.144614	−	0.0834928i	0.570561	+	0.821255i	$0.306726\pi$
$948$		0			0
$949$	−13.4398	+	23.2784i	−0.436274	+	0.755649i
$950$	−20.1810	+	7.30763i	−0.654759	+	0.237091i
$951$		0			0
$952$	8.10015	+	1.98142i	0.262527	+	0.0642181i
$953$	22.9718			0.744131			0.372066	−	0.928206i	$-0.378650\pi$
$953$	22.9718			0.744131			0.372066	+	0.928206i	$0.378650\pi$
$954$		0			0
$955$	53.4541	−	16.5915i	1.72973	−	0.536887i
$956$	−18.8997	−	10.5470i	−0.611260	−	0.341113i
$957$		0			0
$958$	2.53907	−	9.76032i	0.0820336	−	0.315342i
$959$	21.8654	−	37.8720i	0.706072	−	1.22295i
$960$		0			0
$961$	−15.4719	−	26.7982i	−0.499095	−	0.864457i
$962$	−68.9703	+	19.0211i	−2.22369	+	0.613265i
$963$		0			0
$964$	18.7408	−	11.1879i	0.603601	−	0.360337i
$965$	−28.7171	+	31.0592i	−0.924437	+	0.999830i
$966$		0			0
$967$	−21.0871	+	36.5239i	−0.678115	+	1.17453i	0.297433	+	0.954743i	$0.403869\pi$
$967$	−21.0871	+	36.5239i	−0.678115	+	1.17453i	−0.975548	+	0.219787i	$0.929464\pi$
$968$	−4.30280	−	14.7579i	−0.138297	−	0.474337i
$969$		0			0
$970$	8.96618	−	17.3433i	0.287887	−	0.556860i
$971$	29.9678			0.961712			0.480856	−	0.876799i	$-0.340326\pi$
$971$	29.9678			0.961712			0.480856	+	0.876799i	$0.340326\pi$
$972$		0			0
$973$			21.4947i			0.689090i
$974$	15.2188	+	14.9982i	0.487641	+	0.480574i
$975$		0			0
$976$	−8.03573	−	13.0248i	−0.257217	−	0.416915i
$977$	−18.5590	+	32.1452i	−0.593756	+	1.02842i	0.399965	+	0.916530i	$0.369022\pi$
$977$	−18.5590	+	32.1452i	−0.593756	+	1.02842i	−0.993721	+	0.111885i	$0.964311\pi$
$978$		0			0
$979$	9.56383	−	5.52168i	0.305661	−	0.176474i
$980$	−11.9194	+	13.2750i	−0.380750	+	0.424056i
$981$		0			0
$982$	−40.1402	+	11.0701i	−1.28092	+	0.353262i
$983$	24.8903	−	14.3704i	0.793876	−	0.458345i	−0.0474493	−	0.998874i	$-0.515109\pi$
$983$	24.8903	−	14.3704i	0.793876	−	0.458345i	0.841325	+	0.540529i	$0.181776\pi$
$984$		0			0
$985$	−2.59417	+	11.4587i	−0.0826572	+	0.365105i
$986$	−1.45775	−	0.379221i	−0.0464242	−	0.0120769i
$987$		0			0
$988$	−23.3255	−	13.0168i	−0.742084	−	0.414119i
$989$			60.7584i			1.93201i
$990$		0			0
$991$			5.20653i			0.165391i	0.996575	+	0.0826954i	$0.0263529\pi$
$991$			5.20653i			0.165391i	−0.996575	+	0.0826954i	$0.973647\pi$
$992$	0.393862	+	1.28099i	0.0125051	+	0.0406716i
$993$		0			0
$994$	−13.8383	+	53.1953i	−0.438925	+	1.68725i
$995$	41.1067	+	9.30626i	1.30317	+	0.295028i
$996$		0			0
$997$	−18.1724	+	10.4918i	−0.575525	+	0.332279i	−0.759353	−	0.650679i	$-0.774484\pi$
$997$	−18.1724	+	10.4918i	−0.575525	+	0.332279i	0.183828	+	0.982958i	$0.441151\pi$
$998$	−7.84924	−	28.4612i	−0.248463	−	0.900924i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.n.d.179.6		48
3.2	odd	2		180.2.n.d.59.19	yes	48
4.3	odd	2	inner	540.2.n.d.179.10		48
5.4	even	2	inner	540.2.n.d.179.19		48
9.2	odd	6	inner	540.2.n.d.359.15		48
9.7	even	3		180.2.n.d.119.10	yes	48
12.11	even	2		180.2.n.d.59.15	yes	48
15.2	even	4		900.2.r.g.851.7		48
15.8	even	4		900.2.r.g.851.18		48
15.14	odd	2		180.2.n.d.59.6	✓	48
20.19	odd	2	inner	540.2.n.d.179.15		48
36.7	odd	6		180.2.n.d.119.6	yes	48
36.11	even	6	inner	540.2.n.d.359.19		48
45.7	odd	12		900.2.r.g.551.3		48
45.29	odd	6	inner	540.2.n.d.359.10		48
45.34	even	6		180.2.n.d.119.15	yes	48
45.43	odd	12		900.2.r.g.551.22		48
60.23	odd	4		900.2.r.g.851.22		48
60.47	odd	4		900.2.r.g.851.3		48
60.59	even	2		180.2.n.d.59.10	yes	48
180.7	even	12		900.2.r.g.551.7		48
180.43	even	12		900.2.r.g.551.18		48
180.79	odd	6		180.2.n.d.119.19	yes	48
180.119	even	6	inner	540.2.n.d.359.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.6	✓	48	15.14	odd	2
180.2.n.d.59.10	yes	48	60.59	even	2
180.2.n.d.59.15	yes	48	12.11	even	2
180.2.n.d.59.19	yes	48	3.2	odd	2
180.2.n.d.119.6	yes	48	36.7	odd	6
180.2.n.d.119.10	yes	48	9.7	even	3
180.2.n.d.119.15	yes	48	45.34	even	6
180.2.n.d.119.19	yes	48	180.79	odd	6
540.2.n.d.179.6		48	1.1	even	1	trivial
540.2.n.d.179.10		48	4.3	odd	2	inner
540.2.n.d.179.15		48	20.19	odd	2	inner
540.2.n.d.179.19		48	5.4	even	2	inner
540.2.n.d.359.6		48	180.119	even	6	inner
540.2.n.d.359.10		48	45.29	odd	6	inner
540.2.n.d.359.15		48	9.2	odd	6	inner
540.2.n.d.359.19		48	36.11	even	6	inner
900.2.r.g.551.3		48	45.7	odd	12
900.2.r.g.551.7		48	180.7	even	12
900.2.r.g.551.18		48	180.43	even	12
900.2.r.g.551.22		48	45.43	odd	12
900.2.r.g.851.3		48	60.47	odd	4
900.2.r.g.851.7		48	15.2	even	4
900.2.r.g.851.18		48	15.8	even	4
900.2.r.g.851.22		48	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00727 - 0.992675i) q^{2} +(0.0291929 + 1.99979i) q^{4} +(0.493735 - 2.18088i) q^{5} +(-1.65751 - 2.87089i) q^{7} +(1.95573 - 2.04331i) q^{8} +(-2.66223 + 1.70662i) q^{10} +(-1.17952 - 2.04298i) q^{11} +(3.81058 + 2.20004i) q^{13} +(-1.18030 + 4.53714i) q^{14} +(-3.99830 + 0.116759i) q^{16} -0.889368 q^{17} +3.03537i q^{19} +(4.37570 + 0.923698i) q^{20} +(-0.839925 + 3.22872i) q^{22} +(-6.29952 - 3.63703i) q^{23} +(-4.51245 - 2.15355i) q^{25} +(-1.65437 - 5.99870i) q^{26} +(5.69278 - 3.39848i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(0.205172 + 0.118456i) q^{31} +(4.14327 + 3.85140i) q^{32} +(0.895835 + 0.882853i) q^{34} +(-7.07943 + 2.19737i) q^{35} -11.4975i q^{37} +(3.01314 - 3.05745i) q^{38} +(-3.49059 - 5.27407i) q^{40} +(-2.45213 - 1.41574i) q^{41} +(-4.17637 - 7.23369i) q^{43} +(4.05110 - 2.41842i) q^{44} +(2.73494 + 9.91686i) q^{46} +(-6.55796 + 3.78624i) q^{47} +(-1.99467 + 3.45488i) q^{49} +(2.40749 + 6.64861i) q^{50} +(-4.28837 + 7.68457i) q^{52} +0.772055 q^{53} +(-5.03787 + 1.56369i) q^{55} +(-9.10776 - 2.22789i) q^{56} +(1.63908 + 0.426394i) q^{58} +(-1.06446 + 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(-0.0890754 - 0.322986i) q^{62} +(-0.350216 - 7.99233i) q^{64} +(6.67943 - 7.22417i) q^{65} +(-3.17238 + 5.49472i) q^{67} +(-0.0259632 - 1.77855i) q^{68} +(9.31218 + 4.81423i) q^{70} +11.7244 q^{71} +6.10889i q^{73} +(-11.4133 + 11.5811i) q^{74} +(-6.07010 + 0.0886114i) q^{76} +(-3.91012 + 6.77253i) q^{77} +(8.94873 - 5.16655i) q^{79} +(-1.71946 + 8.77744i) q^{80} +(1.06459 + 3.86020i) q^{82} +(-2.25103 + 1.29963i) q^{83} +(-0.439112 + 1.93960i) q^{85} +(-2.97396 + 11.4321i) q^{86} +(-6.48127 - 1.58541i) q^{88} +4.68130i q^{89} -14.5863i q^{91} +(7.08939 - 12.7039i) q^{92} +(10.3642 + 2.69615i) q^{94} +(6.61978 + 1.49867i) q^{95} +(-5.34684 + 3.08700i) q^{97} +(5.43875 - 1.49994i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Introduction

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